When all n teams in a league play every other team twice, a total of N games are played, where N=n2-n-n. A soccer league has 9 teams and all teams play each other twice. How many games are played?
+130517 The ninth team plays the other eight teams twice each.....8 x 2
The eighth team plays the other seven teams twice each......7 x 2
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The second team plays the first team twice....... 1 x 2
So we have
[8 + 7 + 6 + 5 + 4 + 3 + 2 + 1] x 2 =
36 x 2 =
72 games
The answer can also be derived by finding all the possible combinations of any two vertices in a nonagon and multiplying this result by 2 ......thus..... C(9,2) x 2 = 36 x 2 = 72
